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Determining if Two Shapes are Related by Dilation

Determining if Two Shapes are Related by Dilation
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2016-08-16 23:34
PolygonCoordinate Geometry
This example demonstrates how to determine if two polygons are related by dilation, involving core concepts like dilation, coordinate geometry, and similar figures. It uses commands such as Polygon, Dilate, Line, and Point with parameters a, b, c, d, e to construct and analyze the dilation transformation, suitable for high school students learning about properties of similarity transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  2. Dilate(A, 2, F) → A'
  3. Dilate(B, 2, F) → B'
  4. Dilate(C, 2, F) → C'
  5. Dilate(D, 2, F) → D'
  6. Dilate(E, 2, F) → E'
  7. Polygon(A', B', C', D', E') → poly1', a', b', c', d', e'
  8. Line(C', C) → f
  9. Line(D', D) → k
  10. Line(E', E) → l
  11. Line(A', F) → m
  12. Line(B', F) → n
  13. Point(n) → G
  14. Point(m) → H
  15. Point(l) → I
  16. Point(k) → J
  17. Point(f) → K
  18. Polygon(G, K, J, I, H) → poly3, g, k_1, j, i, h
  19. Polygon(L, M, N, O, P) → poly2, l_1, m_1, n_1, o, p
  20. Line(L, A) → q
  21. Line(M, B) → r
  22. Line(P, E) → s
  23. Line(O, D) → t
  24. Line(N, C) → u